Fourier expansions for Eisenstein series twisted by modular symbols and the distribution of multiples of real points on an elliptic curve

This thesis consists of two unrelated parts. In the first part of this thesis, we give explicit expressions for the Fourier coefficients of Eisenstein series E∗(z, s, χ) twisted by modular symbols ⟨γ, f⟩ in the case where the level of f is prime and equal to the conductor of the Dirichlet character χ. We obtain these expressions by computing the spectral decomposition of an automorphic function closely related to E∗(z, s, χ). We then give applications of these expressions. In particular, we evaluate sums such as Σχ(γ)⟨γ, f⟩, where the sum is over γ ∈ Γ∞\Γ0(N) with c^2 + d^2 < X, with c and d being the lower-left and lower-right entries of γ respectively. This parallels past work of Goldfeld, Petridis, and Risager, and we observe that these sums exhibit different amounts of cancellation than what one might expect. In the second part of this thesis, given an elliptic curve E and a point P in E(R), we investigate the distribution of the points nP as n varies over the integers, giving bounds on the x and y coordinates of nP and determining the natural density of integers n for which nP lies in an arbitrary open subset of {R}^2. Our proofs rely on a connection to classical topics in the theory of Diophantine approximation

Meeting Of The Scottish Alpine Botanical Club, 1905, At Killin

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Structural studies of novel hydrogen bonds by x-ray and neutron diffraction.

The first set of measurements in this thesis discusses the hydrogen-bonding behaviour of1,3-dimesitylimidazol-2-ylidene when co-crystallised with organic acids. 1,3-dimesityiimidazol-2-ylidene is an unusual molecule in which it is possible to have a carbon with a valence of two. In the co-crystals of 1,3-dimesitylimidazol-2-ylidene with pentafluorophenol, pentachlorophenol, 2(2-hydroxidophenyl)benzoxazole or 2,6-di-tert-butyl-4-methylpyridine the 1,3-dimesitylimidazol-2-ylidene becomes protonated and uncommonly short C-H - O hydrogen bonds are formed, the shortest has a C-0 separation of 2.800(3)Å. In the 1:1 co-crystal of 1,3-dimesitylimidazol-2-ylidene and diphenylamine the first example of an N-H-C hydrogen bond is observed, with an N-C distance of 3.196(2)Å. The 1:1, 1:2 and 2:1 co-crystals of 4,4'-bipyridine and benzene-1,2,4,5-tetracarboxylic acid(pyromellitic acid) have been studied by X-ray and neutron diffraction and the 1:1 and 1:2 co-crystals of 4,4'-bipyridine and benzene-1,2-dicarboxylic acid (phthalic acid) and the 1:2 co-crystal of bis-1,2-(2-pyridinium)ethane and benzene-1,2-dicarboxylic acid have been studied by X-ray diffraction. In the short N-H- -0 hydrogen bond observed in the 2:1 co-crystal of 4,4'-bipyridine and benzene-1,2,4,5-tetracarboxylic acid (N-0 2.5220(17)Å at 20K) the hydrogen atom was observed to change position with temperature; at 20K the hydrogen lies1.207(3)Å from the nitrogen and 1.325(3)Å from the oxygen and at 296K it has moved across the hydrogen bond to lie 1.240(4)Å from the oxygen atom and 1.302(4)Å from the nitrogen atom. The same phenomenon of temperature dependent proton migration has been observed by neutron diffraction in crystals of pyridine-3,5-dicarboxylic acid and upon deuteration of the hydrogen bonds the magnitude of the effect becomes greater. Solid-state density functional theory calculations have been used to provide theoretical models for the observed behaviour and to predict the inelastic-incoherent neutron-scattering spectra for pyridine-3,5-dicarboxylicacid in different degrees of deuteration

Robert Edward Gross (1905-1988): ligation of a patent ductus arteriosus and the birth of a specialty.

The early 20th century saw an explosion in surgical expertise. Specialties dedicated to delicate organs such as the heart and vulnerable populations, like children, were in their infancy. Dr. William E. Ladd, the father of pediatric surgery, founded the first dedicated department of pediatric surgery at Boston Children’s Hospital in 1910. At the time, attempts at cardiac surgery almost universally ended in death of the patient. The first successful surgical treatment of the cardiac valves would not occur for another 15 years, and the great vessels would remain out of reach for decades more. Dr. Robert E. Gross, the shy and humble heir to the greats of this epoch, would push these embryonic fields into the modern era and train a generation of surgeons to face countless new challenges (Fig. 1)

Hydrophilic, hole-delocalizing ligand shell to promote charge transfer from colloidal CdSe quantum dots in water

Colloidal cadmium chalcogenide nanocrystals are usually stabilized in polar solvents by functionalizing the surface with a layer of hydrophilic ligands. While these ligands protect against aggregation, they also present a steric barrier that hinders surface access. In applications that require charge transfer to and from nanocrystals, colloidal stability and surface access for redox species are therefore difficult to reconcile. This work assesses the possibility of a more dynamic ligand shell that not only provides stability to nanocrystals but also promotes charge transfer without the need for ligand removal. We use transient absorption spectroscopy to study CdSe quantum dots functionalized with hydrophilic, hole-delocalizing dithiocarbamate ligands in water for the first time, and find that a conjugated ligand facilitates charge transfer to redox species in solutio

The Role of Electrode Catalyst Interactions in Enabling Efficient CO2 Reduction with Mo(bpy)(CO)(4) As Revealed by Vibrational Sum-Frequency Generation Spectroscopy

Group 6 metal carbonyl complexes ([M(bpy)(CO)4], M = Cr, Mo, W) are potentially promising CO2 reduction electrocatalysts. However, catalytic activity onsets at prohibitively negative potentials and is highly dependent on the nature of the working electrode. Here we report in situ vibrational SFG (VSFG) measurements of the electrocatalyst [Mo(bpy)(CO)4] at platinum and gold electrodes. The greatly improved onset potential for electrocatalytic CO2 reduction at gold electrodes is due to the formation of the catalytically active species [Mo(bpy)(CO)3]2– via a second pathway at more positive potentials, likely avoiding the need for the generation of [Mo(bpy)(CO)4]2–. VSFG studies demonstrate that the strength of the interaction between initially generated [Mo(bpy)(CO)4]•– and the electrode is critical in enabling the formation of the active catalyst via the low energy pathway. By careful control of electrode material, solvent and electrolyte salt, it should therefore be possible to attain levels of activity with group 6 complexes equivalent to their much more widely studied group 7 analogues

A water-soluble Manganese complex for selective electrocatalytic CO2 reduction to CO

Relatively few solution electrocatalysts for CO2 reduction in aqueous solutions are reported. However to be sustainable, electrocatalytic CO2 reduction is likely to be coupled to water oxidation in a complete device. Here we report a water-soluble Mn polypyridyl complex for the electrocatalytic reduction of CO2 to CO. This complex shows activity across a broad pH range and an excellent selectivity at pH 9 (3.8:1, CO:H2). Cyclic voltammetry indicates activity across a range of different electrode materials (Boron doped diamond, glassy carbon and Hg/Au amalgams)

The city and the senses : urban culture since 1500

This collection of studies, published in the Ashgate Historical Urban Studies series, edited by Richard Rodger and Jean-Luc Pinol, examines ‘urban experience’ though the medium of the five senses: smell, hearing, vision, touch and taste. It draws on a broad range of disciplines, including history, art history, literary criticism, cultural geography and socio-linguistics and brings together young and established scholars from the UK, Ireland and the United States. Editorial responsibility was shared equally with Jill Steward, along with the writing of the introduction, which sets the detailed studies within a theoretical and historiographical context and poses issues for debate. The book contains a single-authored article by Cowan, ‘Not carrying out the vile and mechanical arts: Touch as a measure of social distinction in early modern Venice’. Some of the articles were specially commissioned for this volume. Others were developed from papers given at the International Urban History Conference in Venice in 1998, at a session organised by the Northumbria Research Group for European Urban Culture

Metal-organic conjugated microporous polymer containing a carbon dioxide reduction electrocatalyst

A metal-organic conjugated micorporous polymer (CMP) containing a manganese carbonyl electrocatalyst for CO2 reduction has been synthesised and electrochemically characterised. Incorporation in a rigid framework changes the behavior of the catalyst, preventing reductive dimerization. These initial studies demonstrate the feasibility of CMP electrodes that can provide both high local CO2 concentrations and well defined electrocatalytic sites